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Let's say I have the following animation:

Animate[ParametricPlot[{Cos[a t], Sin[a t]}, {t, 0, 1}], {a, 0, 
  2Pi}, AnimationRate -> 0.1]

Is there a way to somehow zoom into the moving point of the animated plot at a preselected xy-coordinate or time; such as being able to zoom into the animated moving point after 3 seconds or when the moving point reaches {x,y}={-1,0}?

Any help would be appreciated.

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2 Answers 2

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You can make PlotRange a function of any variables you need it to be a function of. I believe how to do it is most clearly explained with code:

f[t_] := With[{a = 2 Pi/20}, {Cos[a t], Sin[a t]}]
plotRangeF[t_, x_] := Which[
  t >= 0 && t < 5, {{0, 1}, {0, 1}},
  t >= 5 && t < 10, {{-1, 0}, {0, 1}},
  t >= 10 && t < 15, {{-1, 0}, {-1, 0}},
  t >= 15 && t <= 20, {{0, 1}, {-1, 0}}
  ]
frame[t_] := Graphics[{
   Point[f[t]]
   }, PlotRange -> plotRangeF[t, f[t]]
  ]
ListAnimate[Table[frame[t], {t, 0, 20, 0.1}]]

I think this may solve your problem. Do note that ParametricPlot also has the PlotRange option.

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  • $\begingroup$ this does not show anything like the original question was asking $\endgroup$
    – am70
    Jul 2, 2023 at 20:20
  • $\begingroup$ @am70 It solved the problem and was accepted. $\endgroup$
    – C. E.
    Jul 2, 2023 at 22:34
  • $\begingroup$ first of all, the code snippet is lacking several semicolons; second and most important, if you run the original code from the OP, you see the animation of a circle that is being drawn; if you run the code from C.E. , it shows a point moving in an abstract space, no circle, no axes, no reference: so it is not even clear if this solution is "zooming" in some sense.. $\endgroup$
    – am70
    Jul 11, 2023 at 11:31
  • $\begingroup$ another weird fact in this solution is that plotRangeF[t_, x_] does not really use x $\endgroup$
    – am70
    Jul 11, 2023 at 13:41
  • $\begingroup$ Let me also add another info: Which will stop at the first matching clause; so it is easier to write Which[ t<5, a, t<10, b...] than Which[ t>0 && t<5, a,t≥5 && t<10, b...] $\endgroup$
    – am70
    Jul 11, 2023 at 14:20
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here is the animation of the OP, but with an initial zoomout, and then tracking of the drawing point

f[x_] := {Cos[2 \[Pi] x ], Sin[2 \[Pi] x ]};
squareF[t_, r_] := {  { f[t][[1]] - r, f[t][[1]] + r} ,
   { f[t][[2]] - r, f[t][[2]] + r} };
plotRangeF[t_] := Which[
   t < 1/6, squareF[t,  5 t + 1/6],
   True, squareF[t,  1]];
frame[t_] := 
  ParametricPlot [f[t x], {x, 0, 1}, PlotRange -> plotRangeF[t]];
animation = ParallelTable[frame[t], {t, 0, 1, 0.01}];
ListAnimate[animation, DefaultDuration -> 10]

squareF defines a square around the moving point, of side 2 r ; changing the Which part in PlotRangeF , you may zoom in and out at will

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